What is the value of the parameter for which we constructed those confidence intervals?

Question

9
5
%
confidence interval for
Lower bound of the interval is
0
.
1
5
6
Upper bound of the interval is
0
.
3
2
4
.
the
9
9
%
confidence interval for your sample.
Lower bound of the interval is
0
.
1
3
0
Upper bound of the interval is
0
.
3
5
0

Answer 1

To determine the parameter value for which the confidence intervals were constructed, we need to identify what value these intervals are estimating.

Given the information about the confidence intervals you've provided:

1. A 95% confidence interval with:

   • Lower bound: \(0.156\)
   • Upper bound: \(0.324\)

2. A 99% confidence interval with:

   • Lower bound: \(0.130\)
   • Upper bound: \(0.350\)

The values of the parameter being estimated (typically a population proportion or mean) would generally fall between these bounds.

You would take the following approach:

Point Estimate Calculation

• For the 95% confidence interval: Calculate the midpoint: \[ \text{Point Estimate (95% CI)} = \frac{0.156 + 0.324}{2} = \frac{0.480}{2} = 0.240 \]

• For the 99% confidence interval: Calculate the midpoint: \[ \text{Point Estimate (99% CI)} = \frac{0.130 + 0.350}{2} = \frac{0.480}{2} = 0.240 \]

Conclusion

Both confidence intervals center around the same point estimate value of \(0.240\). Therefore, the parameter value for which these confidence intervals were constructed is \(0.240\). However, confidence intervals are usually constructed around the point estimate from your sample data, indicating the estimated value of the population parameter.

In summary, the parameter value you likely constructed the confidence intervals for is approximately: \[ \text{Parameter Value} \approx 0.240 \]